Remark 1.3 Although all simplicial buildings have a metrically complete \(\mathrm {CAT}(0)\)  Davis realisation [1]}, \(\mathbb {R}\) -buildings are not necessarily metrically complete, even if they are a Bruhat-Tits building [2]}.
Moreover, the Cauchy completion of an \(\mathbb {R}\) -building is not necessarily an \(\mathbb {R}\) -building [3]}. One can instead use the theory of ultralimits to embed an \(\mathbb {R}\) -building into a metrically complete \(\mathbb {R}\) -building [4]}. However, to prove Corollary REF  we did not need this.

